Dynamic Allocation in Honey Bee and Internet Server Colonies

1
Dynamic Allocation in Honey Bee and Internet
Server Colonies

• Sunil Nakrani, Computing Lab., University of
  Oxford, England, UK
• Craig Tovey, ISyE, Georgia Institute of
  Technology, Atlanta, USA

2
Natural Systems Research Education

• Honey bee colony foraging (Bartholdi, Seeley,
  Tovey VandeVate, J. Th. Bio. 1993) food
  storing to cue nectar intake (Seeley Tovey,
  Animal Beh. 1993)
• Dominance hierarchy formation (Chase, Tovey, et
  al., Proc. Nat. Acad. Sci 2002, Behaviour 2003)
  natural selection mechanism
• Biomimetic heuristic for allocating resources in
  a web-hosting facility (Nakrani Tovey, Proc.
  MASI II, 2003)
• Time lags and overdiscounting of environmental
  costs, hedging value of environmental
  investments replacement policies under
  technological change (Regnier, Sharp Tovey, IE
  Trans.)
• Assessing systems (Tovey, Ausenda) adjusting GDP
  for natural systems deterioration
• Sustainability intro in sophomore course (2030)
  topics course on root causes of env. problems and
  sustainability (4833) stat and design
  sustainability projects

OR -gt BIO
BIO -gt OR
OR -gt ENV
3
Introduction

• Web-Hosting Facility
• Rationale
• Benefits
• Server Allocation Problem allocate servers
  amongst web-apps to maximize revenue
• Honey Bee Colony allocate foragers amongst
  flower patches to maximize nectar intake

4
Introduction

• Approach Honey Bee Heuristics-waggle dance
• Map web-apps to flower patches, servers to bees
• Solution Mapping dance floor--gt advert board
• Algorithms and Simulation Model
• Results
• Conclusions, biological insight
• Future work

5
Web-Hosting Facility
Internet
Hosting Center
Users
Web-App
6
Web-Hosting Model

• Benefits
• Economy of scale Resource sharing means increase
  in utilization and better availability
• Web-App shielded from over-provisioning

7
Web-Hosting Optimisation

• Web-App pay-per-use Service Level Agreement
  (SLA)
• Hosting Center Allocate servers among Web-Apps
  to maximize revenue (s.t. changeover downtime)
• Users Unpredictable and highly variable request
  pattern

8
Web-Hosting Optimisation

• Server Allocation Problem Allocate servers among
  web-Apps to maximize revenue

9
Server Allocation Problem

• Current Techniques Threshold and Ad-hoc Rule
  based, Continuous tracking of load metrics by
  large operations staff, Manual management
• Static provisioning altered approx. once a month
• Current Literature Jayram et. al. (2001), Chase
  et. al. (2001)
• Commercial Domain Proprietary methods

10
Honey Bee Colony

• Approx. 20-50 thousand bees in a colony
• One queen
• Few drones
• Rest workers

11
Honey Bee Colony

• Typically requires 60 lb of honey per year to
  survive
• 25 of workers engaged in food collection
  (nectar, pollen)
• Exploit food sources (flower patches) from
  surrounding countryside

12
Honey Bee Colony

• Flower Patches
• Availability varies daily and seasonally
• Quality depends on exploitation, flower type,
  micro-climate etc..
• Round trip time (nectar collection time)
• Colony Exploit flower patches efficiently to
  satisfy nectar requirement

13
Forager Allocation Problem

• Forager Allocation Problem Allocate forager bees
  among flower patches to Maximize nectar intake

14
Problem Mapping

• Server Allocation Problem
• Single Server
• Web-Apps User
• Group of servers (cluster) serving users at one
  web-app

• Forager Allocation Problem
• Forager Bee
• Flower Patches
• Group of foragers collecting nectar at a specific
  flower patch

15
Problem Mapping

• Server Allocation Problem
• Request service time depends on Web-App
• Find a user to serve

• Forager Allocation Problem
• Travel Time depends on Flower Patch
• Nectar collection time at the patch

16
Problem Mapping

• Server Allocation Problem
• Value-Per-Request-Served
• Varying rates of user request arrivals and
  balking behaviors

• Forager Allocation Problem
• Nectar quality (sugar content)
• Varying flower patch density, quality, and
  replenishment rate

17
Problem Mapping

• Server Allocation Problem
• Server Migration Time (purge current Web-App and
  load new Web-App)

• Forager Allocation Problem
• Time to learn the location of the flower patch
  and successful discovery (Seeley, T.D.)

18
Forager Allocation Mechanism

• Active foragers return to the hive with nectar
  and profitability rating of the visited flower
  patch
• Interact with food-storer bees to offload nectar
  (waiting time provides feedback on nectar flow
  into the hive)

19
Forager Allocation Mechanism

• Feedback sets threshold for enlisting signal
  (Waggle Dance)
• Profitability signal threshold Waggle dance
  duration

20
Forager Allocation Mechanism

• Waggle dance performed just inside the hive
  entrance (Dance floor)
• foragers follow dance to learn flower patch
  location
• Suboptimal allocation in static sense

21
fi(xi) return from xi bees at patch i Max
åi fi(xi) s.t. xi 0 åi xi N

• OPTIMUM
• fi0(xi) l 8 i2 A
• xi 0 8 i Ï A
• equalize marginal return at active patches

• BEE HEURISTIC
• fi(xi)/xi m 8 i2 A
• xi 0 8 i Ï A
• equalize average return at active patches

22
Properties of Heuristic Solution(from BSTV 93)

• Usually not optimal
• Factor-2 approximation even under very weak
  conditions
• Convergence proved by potential function argument
• Validated experimentally in a honey bee colony

23
Solution Mapping

• Server Allocation
• Advert
• Advert Board
• Advert Duration
• Reading an Advert

• Forager Allocation
• Waggle Dance
• Dance Floor
• Dance Duration
• Following Waggle Dance

24
Simulation Model Honey Bee
Web-App A
Post/Read Adverts
Users A
Web-App ID Duration Time
Advert Board
Repurpose
Migrate
Web-App ID Duration Time
Post/Read Adverts
Users B
Web-App B
25
Simulation Model Greedy
Web-App A
Users A
New Policy
Compute optimal policy for next interval based
on present queue status, present allocation,
and user arrival from last interval
Repurpose
Migrate
Users B
New Policy
Web-App B
26
Simulation Model Greedy

• St state of world at start period t
  (customers,servers)
• At arrivals (times, types) in period t
• P(p, S, A) profit using p from state S with
  arrivals A
• f(p,S,A) next state of world using p
• from S with arrivals A
• ptG arg maxp P(p, St, At-1)
• St1 f(ptG, St, At)

27
Simulation Model Others
Web-App A
Users A
New Policy
Offline Omniscient Computation
Repurpose
Migrate
Users B
New Policy
Web-App B
28
Simulation Model Omniscient Optimum

• Sstate, Aarrival, P( )profit, f( )next state
• A1,L, An known
• vn1(Sn1) 0 (no salvage value)
• vt (St) maxpP(p,St,At)
  vt1(f(p,St,At))
• ptOpt(St) arg maxp P(p,St,At)
  vt1(f(p,St,At))

29
Omniscient Optimum Computation

• Parallel implementation runs in 24 hours
• Discretized space of possible states
• Inner loop function that we maximize is
  theoretically concave
• but not concave numerically

30
(No Transcript)
31
Simulation Model Optimal-Static

• Sstate, Aarrival, P( )profit, f( )next state
• A1,L, An known
• s.t. St1 f(p, St, At)

32
Test Case Synthetic User Load
33
Test Case Real Internet Trace
34
Result Synthetic User Load
35
Result Internet Service Trace Load
36
Adaptability to Synthetic Variable Load
37
Synthetic Load Low Variability
38
Conclusions

• Bee heuristic works well, effective in highly
  dynamic environment
• Competitive against standard heuristics
• Bee heuristic Not tuned, Common sense scaling
  parameters used

39
Conclusions

• Trade-off static optimality for responsiveness
• Static optimization requires equalization of
  derivatives (marginal rate bee)
• Bee heuristic has no marginal bee but,
  instead, has ability to migrate several bees at
  the same time and avoids problem of measuring f
  under variability

40
Conclusions
Patch II
Patch I
900
500
Nectar intake increases if
899
501
41
Future Work

• Test to see if we were lucky or robust
• Scale up to more patches/web-apps
• Make autonomic --more feedback loops
• Power imitate indolent bees?
• Convergence rates
• Compare with IBMs online network algorithm

42
Some other interesting stuff

• Dominance hierarchies first experimental
  validation of a self-organizing social structure
  in animals (Chase, Tovey, Martin Manfredonia
  02)
• Time lags of environmental costs mean 10 years
  vs. mean 5 years for other types. (Regnier
  Tovey)
• Opportunities for Sr. Design sustainability
  projects

43
Some Big OR Questions in Natural Systems

• Individual versus group selection classic
  argument against latter is essentially an OR
  proof, but why do forests thrive?
• Discounting and EPV, intergenerational equity
  and intraperiod utility. Relationship to future
  growth? Intraperiod utility and discounting is
  almost equivalent to linear utility, Sobel 2000